Distance Vector

Local Signpost Direction Distance

Routing Table

For each destination list: Next Node Distance

Table Synthesis Neighbors exchange

table entries Determine current best

next hop Inform neighbors

Periodically After changes

dest next dist

Shortest Path to SJ

ij

SanJose

Cij

Dj

DiIf Di is the shortest distance to SJ from iand if j is a neighbor on the shortest path, then Di = Cij + Dj

Focus on how nodes find their shortest path to a given destination node, i.e. SJ

i only has local infofrom neighbors

Dj"

Cij”

i

SanJose

jCij

Dj

Di j"

Cij'

j'Dj'

Pick current shortest path

But we don’t know the shortest paths

Why Distance Vector Works

SanJose

1 HopFrom SJ2 Hops

From SJ3 HopsFrom SJ

Accurate info about SJ ripples across network,

Shortest Path Converges

SJ sendsaccurate info

Hop-1 nodes

calculate current

(next hop, dist), &

send to neighbors

Bellman-Ford Algorithm

Consider computations for one destination d Initialization

Each node table has 1 row for destination d Distance of node d to itself is zero: Dd=0 Distance of other node j to d is infinite: Dj=, for j d Next hop node nj = -1 to indicate not yet defined for j d

Send Step Send new distance vector to immediate neighbors across local link

Receive Step At node j, find the next hop that gives the minimum distance to d,

Minj { Cij + Dj } Replace old (nj, Dj(d)) by new (nj*, Dj*(d)) if new next node or distance

Go to send step

Bellman-Ford Algorithm Now consider parallel computations for all destinations d Initialization

Each node has 1 row for each destination d Distance of node d to itself is zero: Dd(d)=0 Distance of other node j to d is infinite: Dj(d)= , for j d Next node nj = -1 since not yet defined

Send Step Send new distance vector to immediate neighbors across local link

Receive Step For each destination d, find the next hop that gives the minimum

distance to d, Minj { Cij+ Dj(d) } Replace old (nj, Di(d)) by new (nj*, Dj*(d)) if new next node or distance

found Go to send step

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )

1

2

3

31

5

46

2

2

3

4

2

1

1

2

3

5SanJose

Table entry

@ node 1

for dest SJ

Table entry

@ node 3

for dest SJ

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )

1 (-1, ) (-1, ) (6,1) (-1, ) (6,2)

2

3

SanJose

D6=0

D3=D6+1n3=6

31

5

46

2

2

3

4

2

1

1

2

3

5

D6=0D5=D6+2n5=6

0

2

1

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )

1 (-1, ) (-1, ) (6, 1) (-1, ) (6,2)

2 (3,3) (5,6) (6, 1) (3,3) (6,2)

3

SanJose

31

5

46

2

2

3

4

2

1

1

2

3

50

1

2

3

3

6

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (-1, ) (-1, ) (-1, ) (-1, ) (-1, )

1 (-1, ) (-1, ) (6, 1) (-1, ) (6,2)

2 (3,3) (5,6) (6, 1) (3,3) (6,2)

3 (3,3) (4,4) (6, 1) (3,3) (6,2)

SanJose

31

5

46

2

2

3

4

2

1

1

2

3

50

1

26

3

3

4

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (3,3) (4,4) (6, 1) (3,3) (6,2)

1 (3,3) (4,4) (4, 5) (3,3) (6,2)

2

3

SanJose

31

5

46

2

2

3

4

2

1

1

2

3

50

1

2

3

3

4

Network disconnected; Loop created between nodes 3 and 4

5

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (3,3) (4,4) (6, 1) (3,3) (6,2)

1 (3,3) (4,4) (4, 5) (3,3) (6,2)

2 (3,7) (4,4) (4, 5) (5,5) (6,2)

3

SanJose

31

5

46

2

2

3

4

2

1

1

2

3

50

2

5

3

3

4

7

5

Node 4 could have chosen 2 as next node because of tie

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

Initial (3,3) (4,4) (6, 1) (3,3) (6,2)

1 (3,3) (4,4) (4, 5) (3,3) (6,2)

2 (3,7) (4,4) (4, 5) (5,5) (6,2)

3 (3,7) (4,6) (4, 7) (5,5) (6,2)

SanJose

31

5

46

2

2

3

4

2

1

1

2

3

50

2

5

57

4

7

6

Node 2 could have chosen 5 as next node because of tie

3

5

46

2

2

3

4

2

1

1

2

3

51

Iteration Node 1 Node 2 Node 3 Node 4 Node 5

1 (3,3) (4,4) (4, 5) (3,3) (6,2)

2 (3,7) (4,4) (4, 5) (2,5) (6,2)

3 (3,7) (4,6) (4, 7) (5,5) (6,2)

4 (2,9) (4,6) (4, 7) (5,5) (6,2)

SanJose

0

77

5

6

9

2

Node 1 could have chose 3 as next node because of tie

31 2 41 1 1

31 2 41 1

X

(a)

(b)

Update Node 1 Node 2 Node 3

Before break (2,3) (3,2) (4, 1)

After break (2,3) (3,2) (2,3)

1 (2,3) (3,4) (2,3)

2 (2,5) (3,4) (2,5)

3 (2,5) (3,6) (2,5)

4 (2,7) (3,6) (2,7)

5 (2,7) (3,8) (2,7)

… … … …

Counting to Infinity Problem

Nodes believe best path is through each other

(Destination is node 4)

Problem: Bad News Travels Slowly

Remedies Split Horizon

Do not report route to a destination to the neighbor from which route was learned

Poisoned Reverse Report route to a destination to the neighbor

from which route was learned, but with infinite distance

Breaks erroneous direct loops immediately Does not work on some indirect loops

31 2 41 1 1

31 2 41 1

X

(a)

(b)

Split Horizon with Poison Reverse

Nodes believe best path is through each other

Update Node 1 Node 2 Node 3

Before break (2, 3) (3, 2) (4, 1)

After break (2, 3) (3, 2) (-1, ) Node 2 advertizes its route to 4 to node 3 as having distance infinity; node 3 finds there is no route to 4

1 (2, 3) (-1, ) (-1, ) Node 1 advertizes its route to 4 to node 2 as having distance infinity; node 2 finds there is no route to 4

2 (-1, ) (-1, ) (-1, ) Node 1 finds there is no route to 4